Saying they are being crushed by the cost of patients unable to pay, hospital executives rallied Wednesday to back a plan by Gov. Jan Brewer to expand the state’s Medicaid program.

“We’ve seen our uncompensated care close to triple in the last 18 months,’’ said Judy Rich, president and CEO of Tucson Medical Center. “And other hospitals across the state have also struggled under the weight of the dramatic increases of bad debt and charity care.’’

The governor’s plan would impose a tax on hospitals to raise $220 million a year. That would pay the costs for the state to expand eligibility for the Arizona Health Care Cost Containment System, the state’s Medicaid program, to 138 percent of the federal poverty level from its current 100 percent.

That, according to the governor, would add about 240,000 to the AHCCCS rolls. More to the point, it would be done largely with up to $1.6 billion a year the state would get as part of the federal Affordable Care Act.

Brewer acknowledged Wednesday that the details of the hospital tax plan, first announced Monday in her State of the State address, are still being worked out. But that did not stop her from organizing what her staff called a rally of not only hospital executive but also business and economic development officials to build support — and get the governor political cover for the proposal which drew a decidedly cool reception from Republican lawmakers.

The governor said, though, she believes GOP legislators will come around once they understand the impact on Arizona of refusing to become part of what has been called “Obamacare.’’

“They can do the math, it’s pretty simple,’’ she said: More uncompensated care which she said is passed on to businesses and consumers as a $2,000-a-year “hidden tax’’ on families, or taking the federal dollars to relieve the hospitals.

That shift is part of what’s behind the backing for the plan from business groups.

Julie Engel, president and CEO of Greater Yuma Economic Development, said less uncompensated care at hospitals should translate to lower costs for companies that provide health insurance for their workers. And that, she said, will have ripple effects.

“We’re going to see more income churning in the economy because there will be more expenses for food, consumptive goods, because they won’t be having those higher medical bills,’’ Engel said.

And Todd Sanders, CEO of the Greater Phoenix Chamber of Commerce, said the problems of unpaid bills are not simply those of the affected hospitals.

“The reality is when some people receive free care, these costs don’t disappear,’’ he said, but are passed on to someone else. Sanders said higher costs for Arizona businesses make them less competitive globally.

As fast as Brewer is trying to build support for the plan, foes are working to tear it apart.

Tom Jenney, the state director of Americans for Prosperity, disputed savings to business, saying uncompensated care results in “negligible cost shifting’’ to those who purchase health insurance, putting the figure at just 2.8 percent of all health care spending.

But a 2006 report by the Congressional Budget Office — the most recent available with specific numbers — put the figure at 13 percent for government hospitals, 4.7 percent at nonprofit operations and 4.2 percent at for-profit hospitals. Whatever the number, Jenney said if proponents really believe the “hidden tax’’ argument they should guarantee that Arizona families will see a $2,000-a-year cut in health insurance premiums if the state agrees to expand Medicaid.

Jenney acknowledged, though, that his organization, founded with money from brothers David and Robert Koch, who bankroll conservative causes, opposes the federal Medicaid program entirely and, in fact, all government-run health programs.

Brewer, in trying to build support for Medicaid expansion, said lawmakers should not mistake her motives.

“I have never been a supporter of the Affordable Care Act and I am uneasy about the federal government playing such a large role in private individual health care decisions,’’ she said. But the governor said nothing that Arizona could do would eliminate the program.

“It’s the law of the land,’’ she said. “Our decision is whether we will take the action that most benefits Arizona’s families and businesses.’’

Robert Meyer, president of Phoenix Children’s Hospital, said the issues are not just fiscal.

He said the problem with people without insurance and without personal funds to pay for their care is that they do not have access to primary care physicians. Instead they just get sicker and sicker until they finally get to the point where they show up in an emergency room.

“Let me assure you that treating high blood pressure in the emergency room is not going to get you well,’’ Meyer said. “It needs to be at the proper level of care.’’